4. Measuring wellbeing Working in Excel
Excelspecific learning objectives
In addition to the learning objectives for this project, in this section you will learn how to generate new variables using cell formulas.
Part 4.1 GDP and its components as a measure of material wellbeing
Learning objectives for this part
 check datasets for missing data
 sort data and assign ranks based on values
 distinguish between time series and cross sectional data, and plot appropriate charts for each type of data.
The GDP data we will look at is from the United Nations’ National Accounts Main Aggregates Database, which contains estimates of total GDP and its components for all countries over the period 1970–Present. We will look at how GDP and its components have changed over time, and investigate the usefulness of GDP per capita as a measure of wellbeing.
To answer the questions below, download the data and make sure you understand how the measure of total GDP is constructed.
 Go to the United Nations’ National Accounts Main Aggregates Database website. On the righthand side of the page, under ‘Data Availability’, click ‘Downloads’.
 Under the subheading ‘GDP and its breakdown at constant 2010 prices in US Dollars’, select the Excel file ‘All countries for all years – sorted alphabetically’.
 Save it in an easily accessible location, such as a folder on your Desktop or in your personal folder.
 You can see from the tab ‘DownloadGDPconstantUSDcountr’ that some countries have missing data for some of the years. Data may be missing due to political reasons (for example, countries formed after 1970) or data availability issues.
 Make and fill a frequency table similar to Figure 4.1, showing the number of years that data is available for each country in the category ‘Final consumption expenditure’.
 How many countries have data for the entire period (1970 to the latest year available)? Do you think that missing data is a serious issue in this case?
Country  Number of years of GDP data 

Excel walkthrough 4.1 Making a frequency table
If you add up the data on the righthand side of this equation, you may find that it does not add up to the reported GDP value. The UN notes this discrepancy in Section J, item 17 of the ‘Methodology for the national accounts’: ‘The sums of components in the tables may not necessarily add up to totals shown because of rounding’.
There are three different ways in which countries calculate GDP for their national accounts, but we will focus on the expenditure approach, which calculates gross domestic product (GDP) as:
Gross capital formation refers to the creation of fixed assets in the economy (such as the construction of buildings, roads, and new machinery) and changes in inventories (stocks of goods held by firms).
 Rather than looking at exports and imports separately, we usually look at the difference between them (exports minus imports), also known as net exports. Choose three countries that have GDP data over the entire period (1970 to the latest year available). For each country, create a new row that shows the values of net exports in each year. Make sure to give each row an appropriate label.
Now, we will create charts to show the GDP components in order to look for general patterns over time and make comparisons between countries.
 Evaluate the components over time, for two countries of your choice.
 Create a new row for each of the four components of GDP (Household consumption expenditure, General government final consumption expenditure, Gross capital formation, Net exports). To make the charts easier to read, convert the values into billions (for example, 4.38 billion instead of 4,378,772,008). Round your values to two decimal places.
 Plot a separate line chart for each country, showing the value of the four components of GDP on the vertical axis and time (the years 1970–Present) on the horizontal. (Use more than one line chart per country if necessary, to show the data more clearly). Name each component in the chart legend appropriately.
 Which of the components would you expect to move together (increasing or decreasing together) or move in opposite directions, and why? Using your charts from Question 3(b), describe any patterns you find in the relationship between the components. Does the data support your hypothesis about the behaviour of the components?
 For each country, describe any patterns you find in the movement of components over time. What factors could explain the patterns that you find within countries, and any differences between countries (for example, economic or political events)? You may find it helpful to research the history of the countries you have chosen.
 Extension: For one country, add data labels to your chart to indicate the relevant events that happened in that year.
Excel walkthrough 4.2 Adding data labels to a chart
 Another way to visualize the GDP data is to look at each component as a proportion of total GDP. Use the same countries that you chose for Question 3.
 time series data
 A time series is a set of timeordered observations of a variable taken at successive, in most cases regular, periods or points of time. Example: The population of a particular country in the years 1990, 1991, 1992, … , 2015 is time series data.
 crosssectional data
 Data that is collected from participants at one point in time or within a relatively short time frame. In contrast, time series data refers to data collected by following an individual (or firm, country, etc.) over a course of time. Example: Data on degree courses taken by all the students in a particular university in 2016 is considered crosssectional data. In contrast, data on degree courses taken by all students in a particular university from 1990 to 2016 is considered time series data.
 For each country, create a new row in Excel to show the sum of all four components (remember that this total may not add up to the reported GDP). Next, create a new row for each component, showing its proportion of total GDP (as a value ranging from 0 to 1), rounded to two decimal places. (Hint: to calculate the proportion of a component, divide the value of that component by the sum of all four components.)
 Plot a separate line chart for each country, showing the proportion of the component of GDP on the vertical axis and time (the years 1970 to the latest year available) on the horizontal axis.
 Describe any patterns in the proportion of spending over time for each country, and compare these patterns across countries.
 Compared to the charts in Question 3, what are some advantages of this method for making comparisons over time and between countries?
So far, we have done comparisons of time series data, which is a collection of values for the same variables and subjects, taken at different points in time (for example, GDP of a particular country, measured each year). We will now make some charts using crosssectional data, which is a collection of values for the same variables for different subjects, usually taken at the same time.
 Choose three developed countries, three countries in economic transition, and three developing countries (for a list of these countries, see Tables AC in the UN country classification document).
 For each country, calculate each component as a proportion of GDP for the year 2015 only. (You may find it helpful to copy and paste the relevant data into a new Excel sheet.)
 Now create a stacked bar chart that shows the composition of GDP in 2015 on the horizontal axis, and country on the vertical axis. Arrange the columns so that the countries in a particular category are grouped together. (See the walkthrough in Figure 3.8 of Economy, Society, and Public Policy.)
 Describe the differences (if any) between the spending patterns of developed, economic transition, and developing countries.

GDP per capita is often used to indicate material wellbeing instead of GDP, because it accounts for differences in population across countries. Refer to the following articles to help you to answer the questions:
 ‘The economics of wellbeing’ in the Harvard Business Review
 ‘Statistical Insights: what does GDP per capita tell us about households’ material wellbeing?’ in the OECD Insights.
 Discuss the usefulness and limitations of GDP per capita as a measure of material wellbeing.
 Based on the arguments in the articles, do you think GDP per capita is an appropriate measure of both material wellbeing and overall wellbeing? Why or why not?
Part 4.2 The HDI as a measure of wellbeing
Learning objectives for this part
 sort data and assign ranks based on values
 distinguish between time series and cross sectional data, and plot appropriate charts for each type of data
 calculate the geometric mean and explain how it differs from the arithmetic mean
 construct indices using the geometric mean, and use index values to rank observations
 explain the difference between two measures of wellbeing (GDP per capita and the Human Development Index).
In Part 4.1 we looked at GDP per capita as a measure of material wellbeing. While income has a major influence on wellbeing because it allows us to buy the goods and services we need or enjoy, it is not the only determinant of wellbeing. Many aspects of our wellbeing cannot be bought, for example, good health or having more time to spend with friends and family.
We are now going to look at the Human Development Index (HDI), a measure of wellbeing that includes nonmaterial aspects, and make comparisons with GDP per capita (a measure of material wellbeing). GDP per capita is a simple index calculated as the sum of its elements, whereas the HDI is more complex. Instead of using different types of expenditure or output to measure wellbeing or living standards, the HDI consists of three dimensions associated with wellbeing:
 a long and healthy life (health)
 knowledge (education)
 a decent standard of living (income).
We will first learn about how the HDI is constructed, and then use this method to construct indices of wellbeing according to criteria of our choice.
The HDI data we will look at is from the Human Development Report by the United Nations Development Programme (UNDP). To answer the questions below, download the data and technical notes from the report:
 Go to the UNDP’s website.
 Click ‘Table 1: Human Development Index and its components’ to download the HDI data as an Excel file.
 Save the file in an easily accessible location, and make sure to give it a suitable name.
 The ‘Technical notes’ give a diagrammatic presentation of how the HDI is constructed from four indicators.
 Refer to the technical notes and the spreadsheet you have downloaded. For each indicator, explain whether you think it is a good measure of the dimension, and suggest alternative indicators, if any. (For example, is GNI per capita a good measure of the dimension ‘a decent standard of living’?)
 Figure 4.4 shows the minimum and maximum values for each indicator. Discuss whether you think these are reasonable. (You can read the justification for these values in the technical notes.)
Dimension  Indicator  Minimum  Maximum 

Health  Life expectancy (years)  20  85 
Education  Expected years of schooling (years)  0  18 
Mean years of schooling (years)  0  15  
Standard of living  Gross national income per capita (2011 PPP $)  100  75,000 
United Nations Development Programme. 2022. ‘Technical notes’ in Human Development Report 2021/22: p. 2.
We are now going to apply the method for constructing the HDI, by recalculating the HDI from its indicators. We will use the formula below, and the minimum and maximum values in the table in Figure 4.4. These are taken from page 2 of the technical notes, which you can refer to for additional details.
The HDI indicators are measured in different units and have different ranges, so in order to put them together into a meaningful index, we need to normalize the indicators using the following formula:
Doing so will give a value in between 0 and 1 (inclusive), which will allow comparison between different indicators.
 Refer to Figure 4.4 and calculate the dimension index for each of the dimensions in separate columns in the same spreadsheet tab as your data:
 Using the HDI indicator data in Column E, calculate the dimension index for a long and healthy life (health).
 Using the HDI indicator data in Columns G and I, calculate the dimension index for knowledge (education). Note that the knowledge dimension index is the average of the dimension index for expected years of schooling for those entering school, and mean years of schooling for adults aged 25 or older.
 Using the HDI indicator data in Column K, calculate the dimension index for a decent standard of living (income). Note (from the technical notes) that you should calculate the GNI index using the natural log of the values. (See the ‘Find out more’ box below for an explanation of the natural log and how to calculate it in Excel.)
Find out more The natural log: What it means, and how to calculate it in Excel
The natural log turns a linear variable into a concave variable, as shown in Figure 4.5. For any value of income on the horizontal axis, the natural log of that value on the vertical axis is smaller. At first, the difference between income and log income is not that big (for example, an income of 2 corresponds to a natural log of 0.7), but the difference becomes bigger as we move rightwards along the horizontal axis (for example, when income is 100,000, the natural log is only 11.5).
The reason why natural logs are useful in economics is because they can represent variables that have diminishing marginal returns: an additional unit of input results in a smaller increase in the total output than did the previous unit. (If you have studied production functions, then the shape of the natural log function might look familiar.)
When applied to the concept of wellbeing, the ‘input’ is income, and the ‘output’ is material wellbeing. It makes intuitive sense that a $100 increase in per capita income will have a much greater effect on wellbeing for a poor country compared to a rich country. Using the natural log of income incorporates this notion into the index we create. Conversely, the notion of diminishing marginal returns (the larger the value of the input, the smaller the contribution of an additional unit of input) is not captured by GDP per capita, which uses actual income and not its natural log. Doing so makes the assumption that a $100 increase in per capita income has the same effect on wellbeing for rich and poor countries.
Excel’s LN function calculates the natural log of a value for you. Simply type ‘=LN(’, then the number you would like to take the natural log of, then ‘)’ and press Enter. If you have a scientific calculator, you can check that the calculation is correct by using the
ln
orlog
key.
 geometric mean
 A summary measure calculated by multiplying N numbers together and then taking the Nth root of this product. The geometric mean is useful when the items being averaged have different scoring indices or scales, because it is not sensitive to these differences, unlike the arithmetic mean. For example, if education ranged from 0 to 20 years and life expectancy ranged from 0 to 85 years, life expectancy would have a bigger influence on the HDI than education if we used the arithmetic mean rather than the geometric mean. Conversely, the geometric mean treats each criteria equally. Example: Suppose we use life expectancy and mean years of schooling to construct an index of wellbeing. Country A has life expectancy of 40 years and a mean of 6 years of schooling. If we used the arithmetic mean to make an index, we would get (40 + 6)/2 = 23. If we used the geometric mean, we would get (40 × 6)^{1/2} = 15.5. Now suppose life expectancy doubled to 80 years. The arithmetic mean would be (80 + 6)/2 = 43, and the geometric mean would be (80 × 6)^{1/2} = 21.9. If, instead, mean years of schooling doubled to 12 years, the arithmetic mean would be (40 + 12)/2 = 26, and the geometric mean would be (40 × 12)^{1/2} = 21.9. This example shows that the arithmetic mean can be ‘unfair’ because proportional changes in one variable (life expectancy) have a larger influence over the index than changes in the other variable (years of schooling). The geometric mean gives each variable the same influence over the value of the index, so doubling the value of one variable would have the same effect on the index as doubling the value of another variable.
Now that you know about the natural log, you might want to go back to Question 3(c) in Part 4.1, and create a new chart using the natural log scale. The natural log is used in economics because it approximates percentage changes i.e. log(x) – log(y) is a close approximation to the percentage change between x and y. So, using the natural log scale, you will be able to ‘read off’ the relative growth rates from the slopes of the different series you have plotted. For example, a 0.01 change in the vertical axis value corresponds to a 1% change in that variable. This will allow you to compare the growth rates of the different components of GDP.
Now, we can combine these dimensional indices to give the HDI. The HDI is the geometric mean of the three dimension indices (I_{Health} = Life expectancy index, I_{Education} = Education index, and I_{Income} = GNI index):
 Use the formula above and the data in the spreadsheet to calculate the HDI for all the countries excluding those in the ‘Other countries or territories’ category. You should get the same values as those in Column C, rounded to 3 decimal places.
Excel walkthrough 4.3 Calculating the HDI
The HDI is one way to measure wellbeing, but you may think that it does not use the most appropriate measures for the nonmaterial aspects of wellbeing (health and education).
Now we will use the same method to create our own index of nonmaterial wellbeing (an ‘alternative HDI’), using different indicators.
Download alternative indicators to measure health and education:
 Go to the UNDP’s Quality of Human Development data download page.
 Click on the link ‘Download dashboard (Excel)’. It will download the indicator data in Excel format.
 In that spreadsheet, columns CG contain alternative health indicators, and columns IU contain alternative education indicators.
 Create an alternative index of wellbeing:
 Choose two indicators from columns CG to measure health, and two to three indicators from columns IU to measure education. Explain why you have chosen these indicators.
 Carefully copy and paste the column(s) containing these indicator values into new columns of your spreadsheet from Question 4 (containing your HDI calculations), making sure to match the data to the correct country. Choose a reasonable maximum and minimum value for each indicator and justify your choices.
 Using the indicators and maximum and minimum values you have chosen, calculate the alternative HDI as done in Questions 3 and 4. Remember to include the existing income index from Question 2. Since you have chosen more than one indicator per dimension, make sure to average the dimension indices as done in Question 3b. If data for an indicator is unavailable for some countries, use the values of the available indicators to calculate the alternative HDI. Also ensure that higher indicator values always represent better outcomes.
 Create a new column showing each country’s rank according to your alternative HDI, where 1 is assigned to the country with the highest value. Compare your ranking to the HDI rank (Column A). Are the rankings generally similar, or very different? (See Excel walkthrough 4.4 on how to do this.)
Excel walkthrough 4.4 Ranking data
Follow the walkthrough in the CORE video, or in Figure 4.7, to find out how to rank data in Excel.
 Compare your alternative index to the HDI:
 The UN classifies countries into four groups depending on their HDI, as shown in Figure 4.8. Would the classification of any country change under your alternative HDI?
 Based on your answers to Questions 5(d) and 6(a), do you think that the HDI is a robust measure of nonmaterial wellbeing? (In other words, does changing the indicators used in the HDI give similar conclusions about the nonmaterial wellbeing of countries?)
Classification  HDI 

Very high human development  0.800 and above 
High human development  0.700–0.799 
Medium human development  0.550–0.699 
Low human development  Below 0.550 
United Nations Development Programme. 2016. ‘Technical notes’ in Human Development Report 2016: p.3.
We will now investigate whether HDI and GDP per capita give similar information about overall wellbeing, by comparing a country’s rank in both measures. The spreadsheet you downloaded for Question 5 (containing alternative indicators) also has information on GDP per capita, measured in 2011 constant prices in US dollars. This indicator is called ‘GDP per capita (2011 PPP $)’ in Column C of that spreadsheet. To answer Question 7, first filter the data so that only rows containing this indicator are visible, then copy and paste this data into a new column in the spreadsheet containing your HDI calculations, making sure to match the data to the correct country.
 Evaluate GDP per capita and the HDI as measures of overall wellbeing:
 Create a new column showing each country’s rank according to GDP per capita, where 1 is assigned to the country with the highest value. Show this rank on a scatterplot, with GDP per capita rank on the vertical axis and HDI rank on the horizontal axis. (See Excel walkthrough 1.7 for a stepbystep explanation of how to create scatterplots in Excel.)
 Does there appear to be a strong correlation between these two variables? Give an explanation for the observed pattern in your chart.
 Create a table similar to Figure 4.9. Using your answers to Question 7(a), fill each box with three countries. You can use the UN’s definition of ‘high’ for the HDI, as in Figure 4.8, and choose a reasonable definition of ‘high’ for GDP. Based on this table, which country or countries would you prefer to grow up in, and why?
 Explain the differences between HDI and GDP as measures of wellbeing. You may want to consider the way each measure includes income in its calculation (the actual value or a transformation), and the inclusion of other aspects of wellbeing.
HDI  

Low  High  
GDP  Low  
High 
 The HDI is one way to measure wellbeing, but there are many other ways to measure wellbeing.
 What are the strengths and limitations of the HDI as a measure of wellbeing?
 Find some alternative measures of nonmaterial wellbeing that we could use alongside the HDI to provide a more comprehensive picture of wellbeing. For each measure, evaluate the elements used to construct the measure, and discuss the additional information we can learn from it. (You may find it helpful to read Our World in Data’s page on happiness and life satisfaction.)